The Goddess of Small Victories (52 page)

18.
Fermat’s Last Theorem (as the optimists called it) or Fermat’s Conjecture: for any rational number
n
larger than 2, there are no positive nonzero rational numbers
x
,
y
, and
z
such that
x
_n
+
y
_n
= z
_n
. Although mathematicians worked on it for 350 years with mixed results, the theorem was not finally proved until 1995 by Andrew Wiles, a Briton. His proof is frighteningly complex and most certainly does not fit in the margin of any book.

19.
In 1946 the average annual salary in the United States was $3,000.

20.
At the Los Alamos Laboratory, after the first atomic bomb was detonated, Robert Oppenheimer quoted a passage from the Bhagavad Gita: “Now I am become Death, the destroyer of worlds.” To which Kenneth Bainbridge, who directed the testing, answered, “Now we are all sons of bitches.”

21.
Paul Adrien Maurice Dirac (1902–1984) was one of the developers of quantum theory, particularly its mathematical aspects. He predicted the existence of antimatter. With Erwin Schrödinger, he won the Nobel Prize in physics in 1933 “for the discovery of new productive forms of atomic theory.”

22.
Hermann Broch (1886–1951), Viennese novelist and essayist, immigrated to the United States shortly after the Anschluss. Thomas
Mann (1875–1955), who won the Nobel Prize in literature in 1929, was stripped of his German citizenship by the Nazi government. He moved to Princeton in 1939.

23.
After fleeing to Brazil, the Austrian writer Stefan Zweig committed suicide with his wife on February 22, 1942. He dedicated his essay on Freud to Einstein, with whom he was friends.

24.
The World of Yesterday
, an autobiography, was Stefan Zweig’s last work.

25.
In 1946, Albert Einstein became president of the Emergency Committee for Atomic Scientists, whose mission was to inform the public of the dangers of nuclear weapons. The committee was openly against the development of the hydrogen bomb, yet its eight members were all directly or indirectly associated with the Manhattan Project and the making of the first atomic bomb.

26.
Einstein underwent surgery in December 1948 for an abdominal aortic aneurysm. Afterward, a famous photograph was taken, in which he sticks out his tongue. He inscribed a newspaper clipping of the photograph to his surgeon: “To Nissen my tummy, the world my tongue.”

27.
In 1949, Gödel contributed an article to a collection of essays in honor of Albert Einstein’s seventieth birthday: “A Remark About the Relationship Between Relativity Theory and Idealistic Philosophy.”

28.
Years later, his former teacher Hermann Minkowski refined the mathematical foundations of special relativity. Einstein conceded in 1916 that this more “sophisticated” formalization of special relativity had made the discovery of general relativity “much easier.” But this is part of another and extremely complex discussion of the (co)paternity of these theories …

29.
In 1992, the physicist Stephen Hawking formulated a “chronology protection conjecture” to exclude these problematic paradoxes. The philosopher and logician Palle Yourgrau described it as an anti-Gödel conjecture.

30.
To summarize too briefly: the realist philosophers believe that the external world (and phenomena such as time) exist independently of our minds, our knowledge, and our perceptions, whereas the idealist philosophers do not.

31.
The anecdote is supposedly the source of the computer term “bug.” In 1946, ENIAC (Electronic Numerical Integrator and Computer) had a capacity equivalent to 500 FLOPS (Floating-point Operations per Second, a standard measure of the computing ability of a computer). In October 2010, the Tianhe-I, a Chinese supercomputer, achieved calculating speeds of 2.5 petaFLOPS (peta = 10
¹⁵
). Certain researchers have estimated the computational power of the human brain at between 10
¹³
and 10
¹⁹
FLOPS. This extrapolation is based on the number of synapses and neuron connectors, but the age of the individual is not taken into account.

32.
Olga Taussky-Todd (1906–1995): a Czech-American mathematician who was a member of the Vienna Circle and a friend of Kurt Gödel. Amalie Emmy Noether (1882–1935): German mathematician known for her contributions to abstract algebra and theoretical physics. Many consider her the most important woman in the history of mathematics.

33.
Hedy Lamarr (1914–2000): actress, producer, and inventor. With her friend the composer George Antheil, Lamarr patented a system for encrypting transmissions called spread spectrum frequency hopping. The technique is still used for GPS satellite navigation and Wi-Fi connections.

34.
The German word
Dasein
brings together the ideas of being, existence, and presence.
Daseinsanalyse
or “existential analysis” was inspired by the
Daseinsanalytik
of the philosopher Martin Heidegger, who was himself influenced by the phenomenology of his mentor, Edmund Husserl. Hulbeck belonged to the New York Ontoanalytic Association, the U.S. standard-bearer for
Daseinsanalyse
. Gödel’s late
interest in Husserl’s phenomenology is perhaps related to the investigations of his bizarre therapist. The author will not venture a two-line definition of phenomenology.

35.
Huelsenbeck, one of the spokesmen for the Dada movement, called himself “the Drum of Dada.” At the Cabaret Voltaire, the Zurich nightspot where the main figures of Dada performed (Tristan Tzara, Jean Arp, Sophie Taeuber), the future psychoanalyst recited his poetry while accompanying himself on a large drum.

36.
In 1951, Kurt Gödel was the first co-recipient (with Julian Schwinger) of the Albert Einstein Award, in recognition of his contributions to theoretical physics. The award came with $15,000. Von Neumann, one of the jury members with Oppenheimer and Einstein, gave a rousing appreciation of Gödel, calling him a “landmark which will remain visible far in space and time.”

37.
Kurt Gödel was the first logician to receive this honor, awarded to the most eminent scientists.

38.
With his friend Leó Szilárd (himself a physicist on the Manhattan Project), Einstein patented several designs for refrigerators, one of which was based on an “electromagnetic pump.”

39.
Edward Teller (1908–2003), a Hungarian-born physicist, was known for his virulent anticommunism. He is credited with inventing the hydrogen bomb. In the 1980s, as pacifist as ever, Teller was one of the main supporters of Ronald Reagan’s Strategic Defense Initiative, known as “Star Wars,” the satellite-guided laser defense against Soviet nuclear ballistic missiles.

40.
Einstein defied Senator McCarthy, writing in an open letter to the national newspapers: “Every intellectual who is called before one of the committees ought to refuse to testify …”

41.
The FBI compiled a voluminous file on Albert Einstein. Doubtful sources advanced far-flung allegations: he had invented a robot capable of controlling the human mind; one of his sons had been taken
hostage by the USSR. Spurred by J. Edgar Hoover, the immigration service pursued investigations designed to strip Einstein of his American citizenship and expel him from the United States. He remained an American citizen at his death in 1955.

42.
The atomic bomb uses the energy of a nuclear fission chain reaction: the nuclei of heavy atoms (for example, uranium and plutonium) emit energy as they decay into nuclei of lighter weight. The hydrogen bomb (thermonuclear bomb) uses nuclear fusion: energy is released when hydrogen atoms are forcefully brought together to form helium. A helium atom weighs slightly less than the original hydrogen atoms, and the missing mass, according to Einstein’s equation E = mc
²
, turns into energy.

43.
Geeky factoid: Leibniz’s
Nachlass
contains an essay titled “Explanation of Binary Arithmetic, Which Uses Only the Characters 0 and 1,” written more than two centuries before the advent of the computer age.

44.
A remark made by Paul Erdös, a mathematician who was a contemporary of Kurt Gödel.

45.
A quote from the French mathematician Alain Connes, winner of the Fields Medal in 1982.

46.
Roger Wolcott Sperry was an American neurophysiologist. He won the Nobel Prize in medicine in 1981 for his work on the connection between the brain’s two hemispheres.

47.
A quote from Donald Ervin Knuth, a computer scientist and a pioneer of algorithms.

48.
Leonard is here claiming to have invented the RSA cryptosystem, named after Ron Rivest, Adi Shamir, and Leonard Adleman, who first described the system in 1977. Uncrackable, it is still used today for encrypting computer traffic, from online banking to simple e-mails. The discovery of new prime numbers has become a lucrative business: $150,000 for prime numbers of 100 million figures and $250,000 for primes of more than a billion figures.

49.
According to Simon Singh,
The Code Book
.

50.
The message was decrypted seventeen years after its publication by a team of six hundred volunteers. The answer was: “The magic words are squeamish ossifrage.” An ossifrage is a raptor that breaks bones by dropping them from a great height.

51.
The National Security Agency is a U.S. government agency responsible for the collection, analysis, and surveillance of communications.

52.
In 1954, the Supreme Court ruled that the segregation of public schools was unconstitutional. Yet it would take many years and many conflicts before the U.S. educational system enjoyed general desegregation. The first black student at Princeton, Joseph Ralph Moss, was admitted after being demobilized from the U.S. Navy in 1947. He answered to the name “Peat Moss.” David Blackwell (1919–2010) was the first black mathematician to be elected to the National Academy of Sciences.

53.
One of the highest honors awarded to American scientists. Members of the National Academy of Sciences are considered advisers to the nation in science, technology, and medicine.

54.
Lifted from Karl Kraus, Austrian satirist and journalist (1874–1936).

55.
Edmund Husserl (1859–1938) was a German philosopher, logician, and mathematician.

56.
Wolfgang Pauli died in Zurich on December 15, 1958, of pancreatic cancer. While in the hospital, he pointed out his room number to one of his visitors: 137. The number 137 is very nearly the value of the reciprocal of the fine-structure constant, alpha, which is used to measure the electromagnetic force that binds atoms and molecules together. Alpha is calculated from the interaction of photons and electrons. A final instance of the synchronicities so dear to Pauli. Unfortunately, scientists are today reexamining whether alpha is in fact a constant …

57.
John von Neumann died on February 8, 1957, at the age of fifty-three of bone cancer, thought to be the result of radiation exposure during the early nuclear tests. His hospital bed was placed under high surveillance. The information agencies were afraid he would reveal military secrets under the effect of pain medication.

58.
Not until the 1970s would a new generation of physicists (Gabriele Veneziano and Leonard Susskind among them) develop string theory and thus contribute toward a model of quantum gravity. But the Grand Unification or theory of everything remains to this day a white whale.

59.
It has been said that “the father that Hans Albert knew was a man whose combination of intellectual vision and emotional myopia left behind him a series of damaged lives.”

60.
Paul Joseph Cohen (1934–2007) received the Fields Medal in 1966.

61.
Another holy grail of mathematics, the Riemann hypothesis was proposed in the nineteenth century but has still not been entirely resolved. As it treats the distribution of prime numbers, it is relevant to the field of computer encryption.

62.
Cohen devised the powerful mathematical technique called “forcing,” which allows one to demonstrate various relative consistency results. Let us avoid headaches and push the question no farther: the body has its limits.

63.
This document, dated 1970, is included in Kurt Gödel’s
Nachlass
. It comes with no introduction, no commentary, no explanation of the modal system (type of logical grammar) used. Although there is no explicit reference, it seems that this “ontological proof” is based on Saint Anselm’s eleventh-century argument and on the work of Descartes and Leibniz.

64.
“We are far from being able to provide a scientific basis for
the theological worldview, but I believe it would be possible to show by purely rational argument (without relying on any religion’s faith) that the theological vision of the world is perfectly compatible with all known facts (including the objects that rule over this world).”—Kurt Gödel, letter to Marianne Gödel, 1961